If $x \odot y = xy+2x-y$ and $x \barwedge y = 4x-8y$, find $(-2 \odot 2) \barwedge -2$.
Solution: First, find $-2 \odot 2$ $ -2 \odot 2 = (-2)(2)+(2)(-2)-2$ $ \hphantom{-2 \odot 2} = -10$ Now, find $-10 \barwedge -2$ $ -10 \barwedge -2 = (4)(-10)-(8)(-2)$ $ \hphantom{-10 \barwedge -2} = -24$.